All?gre Claude J. Isotope Geology

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PREFACE

Isotope g eology is the o¡springofgeologyon one hand and ofthe conceptsand methods of

nuclear physicsontheother. Itwasinitiallyknown as‘‘nucleargeology’’andthen as‘‘isotope

geochemistry’’ before its currentname of isotope geolog y came tobe preferred because itis

based on the measurementand interpretation ofthe isotopic compositionsofchemicalele-

ments making up the various natural systems.Variations in these isotope compositions

yield useful information for the geological sciences (in the broad sense). The ¢rst break-

through for isotope geology was the age determination of rocks and minerals, which at a

stroketransformedgeology into aquantitative science.Nextcame the measurementofpast

temperatures and the b irth of paleoclimatology.Then horizons broadened with the emer-

genceofthe conceptofisotopictracersto encompassnotonlyquestionsoftheEarth’sstruc-

tures and internaldynamics, oferosion, and ofthe tran sportof material, but also problems

ofcosmochemistry, includingthoserelating to the origins ofthe chemical elements. Andso

isotopegeologyhas notonlyextended across the entire domain ofthe earthsciencesbuthas

also expandedthat domain, opening up many newareas,from astrophysicsto environmen-

talstudies.

This book is designed to provide an introduction to the methods, techniques, and main

¢ndings of isotope geology.The general characterofthe subjectde¢nes its potential reader-

ship: ¢nal-year undergraduates and postg raduates in the earth sciences (or environmental

sciences), geologists, geophysi cists, orclimatologistswantinganoverviewofthe ¢eld.

This is an educational textbook.To my mind, an educational textbook must set out its

subject matter and explain it, but it must also involve readers in the various stages in the

reasoning. O ne cannot understand the development and the spirit of a science passively.

The reader must be active.This book therefore makes constant use ofquestions, exercises,

and problems. I have sought to write a bookon isotope geology in the vein of Turcotte and

Schubert’s Geodynamics (Cambridge University Press) or Arthur Beiser’s Concepts of

ModernPhysics (McGraw-Hill),wh ichtomymindare exemplary.

As it is an educational textbook,information is sometimes repeated in di¡erent places. As

modern research in the neurosciences shows, learn ing is based on repetition, and so I have

adopted this approach. This is why, for example, although numerical constants are often

given in the maintext, manyofthem arelisted again in tables atth e end. Inother cases, I have

deliberately notgivenvalues sothat readers will haveto lookthemup for themselves, because

informationonehasto seekoutisrememberedbetterthan informationserveduponaplate.

Readers must therefore work th rough the exercises, failing which they may not fully

understand how theideasfollowon from one another. Ihavegiven solutions aswego along,

sometimes in detail, sometimes more summarily. At the end of each chapter, I have set a

numberofproblemswhosesolutions canbefoundatthe endofthebook.

Another message I want to get across to students of isotope geology is that this is not an

isolated discipline. It is immersed both in the physical sciences and in the earth sciences.

Hence the deliberate use h ere and there of concepts from physics, from chemistry

(Boltzmann distribution,Arrhenius equation,etc.),orfromgeology(platetectonics,petro-

graphy, etc.) to encourage study of these essential disciplines and, where need be, to make

readers look up information in basic textbooks. Isotope geology is the outcome of an

encounter between nuclear physics and geology; this multidis ciplinary outlook must be

maintained.

Thisbookdoesnotsetouttoreviewallthe resultsofisotopegeologybuttobring readersto

apoint wheretheycan consultthe original literature directlyand withoutdi⁄culty. Among

cur rent literature on the same topics, this book could be placed in the sam e category as

Gunter Faure’s Isotope Geology (Wiley), to be read in preparation for Alan Dickin’s excel-

lent Radiogenic IsotopeGeology (Cambridge Univers ity Press).

The guideline I have opted to follow hasbeen to l eave aside ax iomatic exposition an d to

take instead a didactic, stepwise approach.The ¢nal chapter alone takes a more synthetic

perspective, whilegiving pointersfor future developments.

I have to give a warning about the references. Since this is a book primarily directed

towards teaching I have notgiven a full setof references for each topic. I have endeavored to

give due creditto the signi¢cant contributors withthe properorderofpriority (which is not

always the case in modern scienti¢c journals). Becau se itis what I am most familiar with, I

have made extensive u se ofworkdone in my laboratory.Th is leads to excessive emphasis on

my own laboratory’s contributions in some chapters. I feel sure my colleagues will forgive

meforthis.Th e referencesattheendofeachchapteraresupplementedbyalistofsuggestions

for further reading atthe end ofthebook.

x Preface

ACKNOWLEDGMENTS

Iwould liketothank allthose whohavehelped mei n writingthisbook.

Mycolleagues Be rnardDupre

,Bruno Hamelin, E

ric Lewin, Ge

rard M anhe

s, and Laure

Meynadier made many suggestions and remarks right from the outset. Didier Bourles,

Serge Fourcade, Claude Jaupart, and Manuel Moreira actively reread parts of the

manus cr ipt.

I am grateful too to those who helped in producing the book: Sandra Jeunet, who word-

processed a di⁄cult manuscript, Les E

ditions Belin, and above all Joe

l Dyon, who did the

graphics. Christopher Sutcli¡ehasbeena mostco-operativetranslator.

My verysi ncere thanks to all.

CHAPTER ONE

Isotopes and radioactivity

1.1 Reminders about the atomic nucleus

Inth e model ¢rst developed by Niels Bo hr and Ernest Rutherford an d extended byArnold

Sommerfeld, the atom is composed of two entiti es: a central nucleus, containing most of

the mass, and an array oforbiting electrons.

The nucleus carries a positive charge of þZe,

which is balanced by the electron cloud’s negative charge of Ze.The number of protons,

Z, is matchedin an electricallyneutralatombythe numberofelectron s.Eachoftheseparti-

cles carries anegative electric chargee.

As a rough description, the nucleus of any element is made up of two types of particle,

neutrons and protons. A neutron is slightly heavier than a proton with a mass of

¼1 . 674 95  10

27

kg compared with m

¼1.672 65  10

27

kg for the proton.While of

similar masses, then, the two particles di¡er above all in thei r charges. The proton has a

positive charge (þe) while the neutron is electrically neutral.The number of protons (Z)is

the atomic number.The sum A ¼N þZ of the number of neutrons (N) plus the number of

protons (Z) gives the mass n u mber. This provides a measure of the mass of the nuclide in

question if we take as our unit the approximate mass of the neutron or proton. Thoms on

(1914)andAston(1919)showedthat,foragivenatomicnu mberZ,thatis,foragivenposition

in Mendeleyev’s periodic table, there are atoms with di¡e rent mass numbers A,andthere-

fore nuclei which di¡er i n the number of neutrons they contain (see Plate1). Such nuclides

areknown as theisotopes ofan element.

Thus thereis oneform ofhydrogenwhos e nucleus is composed of justa single proton and

another form of hydrogen (deuterium) whose nucleu s comprises both a proton an d a n eu-

tron; these are the two stable isotopes of hydrogen. Most elements have several naturally

occurring isotopes. However, some, including sodium (Na), aluminum (Al), manganese

(Mn), and niobium ( Nb), havejustonenatural,stable isotope.

The existen ceofisotopeshasgiven risetoaspecial formofnotationfor nuclides.Thesym-

bolofthe element ^ H,He,Li,etc.^ iscompletedbytheatomic numberandthemassnumber

Li;

Li, etc.This notation leavesthe right-hand side ofthesymbol free for chemi-

cal notations used for molecular or crystalline compounds such as

:The notation

atthelowerleftcanbeomittedas itduplicatesthelettersymbolofthe chem icalelement.

For the basic concepts of modern physics the exact references of original papers by prominent ﬁgures

(Einstein, Fermi, etc.) are not cited. Readers should consult a standard textbook, for example Leighton

(1959) or Beiser (1973).

The discover y of isotopes led immediately to that of is obars. These are at oms with the

same mass numbers but with slightly di¡erent numbers of protons.The isobars rubidium

Rb and str ontium

Sroralternatively rhenium

187

Re and osmium

187

Osdo notbelong in

the same slots inthe periodic table and so are chemicallydistinct. It is importanttoknowof

isobarsbecause,unlesstheyareseparated chemic allybeforehand, they‘‘interfere’’withone

another when isotope abundances aremeasuredwitha mass spectrometer.

1.2 The mass spectrometer

Just astherewouldbeno crystallography withoutx-rays norastronomy withouttelescopes,

so there would be no isotope geology without the invention of the mass spectrometer.This

wasthe major contributionof Thom son (1914)andAs ton (1918). Astonwonthe1922 Nobel

Prize for chemistry for developing this instrument and for the discoveries itenabled him to

make.

Subsequent improvements were made by Ba inb r i dge and Jordan (1936), Ni e r

(194 0), and Ingh ram and Chupka (1953). Major improvements have been made using

advances in electronics and computing. A decisive step was taken by Arriens and

Compston(1968)andWasserburgetal.(1969)inconnectionwithMoonexplorationwith

the development of automated machines. More recent commercial machines have

improvedquality, performance, andreliability tenfold!

1.2.1 The principle of the mass spectrometer

The principle is straightforward enough. Atoms of the chemical element whose isotopic

composition is to be measured are ionized in a vacuum chamber. The ions produced are

then accelerated by using a potential di¡erence of 3^2 0 kV. This produces a stream of

ions, an d so an electric current, which is passed through a magnetic ¢eld. The magnetic

¢eld exerts a force perpendi cular to the‘‘ionic current’’and so bends the beam of ions.The

lighter ions are de£ected more than the heavier ones and so the ions can be sorted accord-

ing to their masses.The relative abundance ofeach isotope can be measured from the rela-

tive values of the electron currents produced by each stream of ions separated out in this

way.

Let us put this mathematically. Suppose atoms of the element in question have been

ionized.The ionacceleration phase is:

eV ¼

where eV is theelectricalenergy,

isthekinetic energy,e isthe ion’s charge, v itsspeed, m

its mass,and V thepotentialdi¡erence. Itcanbe deducedthat:

v ¼

2eV



The other inventor of the mass spectrometer, J. J. Thomson, had already been awarded the 1906 Nobel

Prize for physics for his discovery of the electron.

2 Isotopes and radioactivity

Magnetic de£ection is givenbyequating the magnetic force Bev to centripetal acceleration

/R) multiplied by mass m,whereB is the magnetic ¢ eld and R the radius of curvature of

the de£ectedpath:

Bev ¼ m



Itcanb ededuc edthat:

v ¼

BeR

Makingthetwovaluesofvequal,whichistantamounttoremovingspeedfromthe equation,

gives:

ThereforeR isproportionalto

ﬃﬃﬃﬃ

,foranion ofagiven charge.Allowingforelectron charge,

elementalmass,

and di¡erences inunits, we canwrite:

m ¼

20 721 V

 10

inwhichB is in teslas,m inatom ic massunits, R in meters,andVinvolts.

Exercise

A mass spectrometer has a radius of 0.3 m and an acceleration voltage of 10 000 V. The

magnetic ﬁeld is adjusted to the various masses to be measured. Calculate the atomic mass

corresponding to a ﬁeld of 0.5 T.

Answer

Just apply the formula with suitable units:

ð0:5Þ

ð0:3Þ

20 721 ð10

 10

¼ 108:58:

Exercise

If hydrogen ions (mass number ¼1) are accelerated with a voltage of 10 kV, at what speed are

they emitted from the source?

Answer

Just apply the formula

¼ð2e

. The electron charge is 1.60219  10

19

coulombs and

the atomic mass unit is 1.660 540 2  10

27

kg.

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1:9272  10

¼ 1388 km s

1

Atomic mass unit: m ¼1.660 540 2  10

27

kg, electron charge: e ¼1.602 19  10

19

C, therefore

e/m ¼0.964  10

Ckg

1

(C ¼coulomb).

3 The mass spectrometer

which is about 5 million km per hour. That is fast, admittedly, but still well below the speed of

light, which is close to 1 billion km per hour! Heavy ions travel more slowly. For example ions

¼100 would move at just a tenth of the hydrogen speed.

1.2.2 The components of a mass spectrometer

The pri ncipal components ofa mass spectrometer are the source, the magnet, and the col-

lectorand measurementsystem s, allofwhichare maintainedunder vacuum.

T he source

Thesource has threefunctions:



Togenerateions fromatoms.The ions maybepositiveor negative.



To accelerate the ion by potential di¡erences created by plates at di¡erent potentials

(from groundto20 KeV, andin ac celerator massspectro meters toseveralMeV).



To shapethebeam, through calibrated slits inthe high-voltage plates.Thebeam fro m the

source slitisusually rectangular.

The magnet

The magnet has two functions. It deviates the ions and this de£ection separates them by

mas s. Atthe same time ittreats the various compon ents ofthe ion beam or a single mass as

an optical instrument would. It handles both colors (masses) and alsobeam geometry. One

of itsproperti es is tofocus each ionbeam for each mass on the colle ctor.The characteristics

offocusing vary with the shape ofthe magnet and the shape ofth e pole face, which may be

cur ved invarious ways (Figure1.1 and Plates 2 and 3). A fu rther recent improvement, using

computer simulation, hasbeen tofo cus thebeam notonlyi n thex and ydirectionsbutin the

z directiontoo. In modern solid-source mass spectrometers, the angu lardispersion of ions

is fully c orrected and almost all the ions leaving the source end up in the collectors which

arearrangedin afocal plane.

The col lectors

The collectors collect and integrate the ion charges so generating an electric current. The

collectormaybeaFaradaybucket,whichcollectsthe chargesandconvertsthemintoacurrent

that is conducted along awire to an electrical resistor. By measuring the potential di¡erence

across the resistor terminals, the current can be calculated from Ohm’s law, V ¼IR.The

advantage is that it is easy to amplify a potential di¡erence electronically. It is convenient to

workwithvoltages ofabout1V. As the currentstobe measured rangefrom10

11

to10

9

A, by

Ohm’s law, the resistors commonly used range from 10

to 10

. This conversion may be

made for small ion £uxes of electron m ult ipli er s or ion counters.

In all cases the results are

obtaine d by collecting the ion charges and measuring them. Just ahead of the collector

system is a slit that isolates the ion beam. This is explained below.

Each ion pulse is either counted (ion counter) or multiplied by a technical trick of the trade to give a

measurable current (electron multiplier).

4 Isotopes and radioactivity

The vacuu m

A fou rth imp ortantcomponentis thevacuum. Ions cantravel from the source tothe collec-

tor only if they are in a vacuum. Otherwise they will lose their charge by collision with air

molecules and return to the atom state. The whole system is built, then, in a tube where a

vacuum can be maintained. In general, a vacuum of 10

7

millibars is produced n ear the

source and another vacuum of10

9

millibarsor better near the collector. Even so, some air

Magnet

Amplifier

ION SOURCE COLLECTOR

Filament

High voltage

Faraday

cup

Intensity (V )

Strontium

STRONTIUM ISOTOPES

88878684

x33

x10

Figure 1.1 A thermal-ionization mass spectrometer. Top: in the center is the electromagnet whose ﬁeld

is perpendicular to the ﬁgure and directed downwards (through the page). By Fleming’s rules, the force

is directed upwards (towards the top of the page) since the stream of ions is coming from the left. An

array of Faraday cups may be used for multicollection, that is, for simultaneous measurement of the

current produced by each isotope. One important feature has been omitted: the whole arrangement is

held in a vacuum of 10

7

–10

9

mm Hg.

Bottom: the mass spectrum of strontium.

The SI unit of pressure is the pascal (Pa) but for a time it was measured by the height expressed in

centimeters (cm) of a column of mercury in reference to Torricelli’s experiment. This unit has been used

ever since for measuring extreme vacuums. ‘‘Standard’’ atmospheric pressure of 10

Pa corresponds to

76 cm of mercury.

5 The mass spectrometer

molecules rem ain inside the mass spectrometer and col lide with the beams, partially

disruptingtheir initialrectangular section.

All of these components contribute to the quality of the data obtained. Mass spectro-

meter qualityis characterizedbyanumberoffeatures.

E⁄ci ency

This isgivenbythe ratio

Number of ions collected

Number of atoms in source

¼ E

Number of ions ¼ intensity  duration 

6:24  10

Z ion charge

Number of atoms ¼

mass

atomic mass

 Avogadro’s number:

E⁄ci ency varieswithatomic mass.

Ionization e⁄ciency of the source (I) and transmission e⁄ciency of the total ion

optics (T):

I  T ¼ E

ThevalueofTis variable:1% for ICP-MS,25%for ion probes.

The values of I have been g reatly improved but vary with the nature of the element and

the ionizationprocess.The rangeis 5%

to100% (ICP-MS)!

Power of resolution

The question is, whatis the smallest di¡erence in mass that canbe sep arated and then mea-

suredusinga mass spectrometer? A formalde¢nition is:

Figure 1.2 (a) Incident beam in the focal plane. (b) Magnet focalization. The beam from the source has a

certain aperture. The trajectories of some ions that are not strictly perpendicular to the source are

refocused by the magnetic ﬁeld. The refocusing surface for the various masses at the collector end is

curved if the magnet faces are plane, but may be plane if a curved magnet face is used. The ﬁgure shows

schematically how the magnet separates three isotopes in both conﬁgurations.

6 Isotopes and radioactivity